Evaluation of the Effect of Anterior Teeth Torque Values on the Space Occupied by Six Anterior Teeth: a Finite Element Analysis

Statement of the Problem: Various factors have been introduced to achieve normal occlusion. One of them is anterior teeth torque that has a significant effect on orthodontic treatment outcomes. Purpose: The aim of this study was to investigate the effect of changes in anterior teeth torque on changes in the space occupied by six anterior teeth by using computer-aided three-dimensional interactive application (CATIA). Materials and Method: In this experimental finite element study, acrylic teeth with pre-adjusted MBT braces were aligned and three-dimensional (3D) scans were made by 3Dscaner. In the CATIA software program, upper incisors’ torque was changed to -2, -4, -6, +2, +4 and+6 degrees and in the lower incisors to -1, - 3, -5, +3 and+5 degrees; the space was measured at 3 heights of maxillary incisor crowns and at incisal edges of mandibular incisors. Then maxillary incisors were then tapered and the measurements were made again. To evaluate the effect of tooth size, these procedures were carried out on teeth with +17% and -17% magnifications. Results: The results showed that by increasing anterior torque from 14.7 to 20.7 degrees in maxillary incisors, the space occupied by anterior teeth increased. Maximum changes were at cingulum height with 1.421mm. Reduction in anterior torque from 14.7 to 8.7 degrees resulted in a decrease in this space and maximum changes were observed in the cingulum height with 1.824mm. In the mandibular arch, a 10-degree change in anterior torque resulted in an -.752mm change in the space. Changes in the space occupied by anterior teeth was not significant in tapered and normal teeth in +6 and -6-degree torque (p Value= 0.78 and p Value=0.83). Conclusion: By increasing or decreasing the incisors’ torque, the space occupied by anterior teeth increased and decreased, respectively. These changes were less in tapered teeth. Size variations had no significant effect on the results.


Introduction
Orthodontic treatment aims to achieve dentofacial esthetics and ideal jaw function. One of the most im-portant factors in achieving this goal and resolving the patients' problems is to achieve proper occlusion. Proper positioning of all the teeth is necessary to form stable and functional occlusion and to position the teeth in a proper relationship with each other and in equilibrium with maxillofacial soft and hard tissues [1][2][3].
In 1963, Dempster et al. [1] evaluated the inclination of the long axis of teeth in eleven skulls with normal occlusion and reported that all the teeth had an inclination relative to the occlusal plane, which was necessary for achieving the best function.  [2][3][4] (Figure 1). In addition, the crown torque clearly affects the overbite and overjet.
The torque of the maxillary incisors is particularly important in creating a beautiful smile line, proper anterior guidance, and a stable class I relationship because incisors with inadequate torque (under torque) prevent distal movement of anterior dentition [2][3]. In the cartwheel model of Andrew, a number of vertical wires are soldered on a rectangular arch, as anterior teeth. When the anterior segment of the arch is affected by lingual torque, the vertical wires become convergent so that when the torque is applied at a 90º angle, the wires can be considered as the spokes of a wheel [2] (Figure 2).
O'Higgins et al. [5] evaluated the effects of the torque of maxillary incisors on the dental arch space.
They used Typodont acrylic resin teeth and natural maxillary incisors with different torques. Then impressions were taken from the set-ups. A reflex microscope was used to measure the arch length from the first incisors on the cast. They concluded that the arch length increased approximately 1mm with a 5-degree increase in the torque of incisors.    [5], torque values were not changed in arranged intervals and simulation of clinical situation was made with less effort.
Considering the importance of the torque of tooth crowns in achieving proper occlusion and the limitations of previous studies [2,[4][5], the present study was conducted to quantify the effects of the torque of anterior teeth on the treatment outcomes, with the use of more accurate techniques, and to evaluate the effects of changes in the torque of anterior teeth on the space occupied by six anterior teeth.

Materials and Method
In the present study, three-dimensional (3D) scanning of the samples was prepared from Typodont acrylic resin teeth and analyses with computer-aided threedimensional interactive application (CATIA) (Dassault systems, France) were used to evaluate the changes in the torque and the form of the tooth crown. The teeth were sectioned in the software program and  forces that should be applied to achieve the torque values ( Figure 6).
Subsequently, a number of wire elements were considered as fixed points and opposing (couple) forces were applied to the wires ( Figure 7). The built-in torque in MBT brackets is 17º; as a result, 25*21 steel arch wire, with a freedom of 2.33º, applies a torque of 14.7º to the incisor teeth [7]. Torque values applied to the maxilla to evaluate changes in the spaces occupied by six anterior teeth were +2, +4, +6, -2, -4, and -6.
To make the study more relevant clinically, a decision was made to evaluate changes in the spaces occupied by six anterior teeth with the limits of the line of occlusion. Concerning the differences in the overbite in the normal range of overbite, measurements were carried out at three heights of the crowns of upper incisors.
To this end, the distance from the incisal edge to the cingulum was divided into three equal heights using planes that crossed from the distal aspect of the canine sharp line angles and t are more tapered from incisal to cervical. Therefore, the cervical region of triangular teeth is narrower. In ovoid teeth, connector is located more incisally and contact point is small. In triangular teeth, incisal embrasure is smaller. The CATIA software program was used to reconstruct the tapered shape of crown by changing the size, the location of the connector, and the size of the incisal embrasure. Then again, the procedures for changing the torque and for measuring  Finally, since the maximum and minimum widths of normal maxillary central incisors have been reported to be 9.6 and 7.2 mm, respectively, in order to evaluate the effect of tooth size on changes in space resulting from changes in the arch, the measurements on the scanned samples of the upper jaw were repeated with 17% of magnification and 17% of decrease in size and the results were reported [10][11] (Figure 11).

Statistical analysis
Data were transferred to Excel and SPSS 18 software programs and classified, summarized, and adjusted using proper methods and presented in the form of tables.
Independent-samples t-test was used to compare changes in the spaces occupied in terms of crown form. Significant differences were defined as a p< 0.05.  (Table 1, 2, Figure 12).

Tables 1 and 2 present the numeric values of spaces oc-
Based on the data collected in the upper jaw at +6 and -6 torque degrees, the spaces occupied by anterior teeth in the cingulum area in case of increased bite, changed from 32.424 to 30.842mm ( Table 3). The amount of change in the mesiodistal inclination of the teeth measured with a change in torque was measured. It was shown that there was 0.92° of mesial tipping of the root with each 4° increase in the lingual torque of the root.
Based on the results, in the lower jaw, the spaces occupied by the lower teeth at the incisal edge changed 0.752 mm from +5 to -5 degrees (Table 4).     (Table 5).
In addition, at +6 and -6 degrees, the spaces occupied by upper anterior teeth in the middle area at 17% magnification changed 1.202 and -0.77 mm, respectively, with changes of 1.06 and -0.58 mm at -17% magnification, respectively (Table 6).

Discussion
Considering only geometric measurements were used, which might not be extended to clinical conditions. Furthermore, in order not to complicate the results in Nanda and Hussel study [4], the numbers of elements were few and normal    should be considered during diagnosis, treatment planning, and determination of the prognosis of orthodontic treatment [9,11]. Despite 20-30% prevalence of anterior Bolton discrepancy [12][13][14], an important consideration is the fact that such a difference in tooth sizes, which is <2 mm and is achieved through Bolton analysis, is not clinically important [15]. However, if the torque of the anterior teeth is not properly managed during treatment, the effect of inadequate torque is added to the effect of anterior Bolton discrepancy, resulting in aggravation of problems associated with space closure and achievement of solid occlusion.
For example, according to Araujo et al. [16], the mean anterior Bolton discrepancy in class II subjects is 78.16%. Considering the normal amount of anterior Bolton discrepancy, which is 77.2% [17], it might be claimed that the amount of discrepancy in the size of teeth in such individuals is approximately 0.4-0.5 mm.
Since such a discrepancy is negligible clinically, it is possible that a sizeable proportion of patients, in which the space discrepancy during treatment is attributed to Bolton discrepancy, have in fact a combination of mild Bolton discrepancy and decreased torque of the anterior teeth.
On the other hand, the results of the present study showed that an increase in overbite resulted in a 1.82mm decrease in the space occupied by anterior teeth.
Therefore, in cases in which an increase in overbite is concomitant with a decrease in the torque in anterior teeth and with possibly Bolton discrepancy, major problems might occur during orthodontic treatment.
In patients with class II div2 malocclusion, there is a combination of increased overbite and incisors with decreased torque. In addition, there is a strong relationship between class II div2 malocclusion and developmental anomalies of teeth, resulting in a 3-fold increase in the incidence of these anomalies in subjects with class II div2 malocclusion compared to the general population. There is a statistically significant decrease in the mesiodistal width of permanent incisors in subjects with this malocclusion, resulting in Bolton discrepancy [18].
The mean Bolton discrepancy in these subjects has been reported to be 83%. The excess tooth mass in the anterior segment of the mandible or tooth mass deficiency in the anterior segment of the maxilla might even be approximately 2 mm. Therefore, in some of these individuals, association of Bolton discrepancy and decreased torque might give rise to the aggravation of problems in achieving normal occlusion during treatment. Therefore, in these subjects it is necessary to pay attention to the presence and amount of Bolton discrepancy and decreased torque before undertaking treatment in proper treatment planning and by extracting mandibular incisors if necessary [17].
In these cases, en-masse anterior retraction might exacerbate decreased torque, leads to termination of treatment with class II canine relationship and the absence of overjet. In some of these patients, use of techniques that preserve and correct anterior torque, such retraction of canines separately and use of closing loops with torque for anterior retraction seem necessary for ideal termination of treatment. In addition, use of arch wires with exaggerated curve of spee in growing subjects might be useful [19].
In cases in which retraction of anterior teeth is carried out by skeletal anchorage (mini screws), usually the line of action of force crosses the lower part of the resistance center of the anterior segment, which results in the loss of torque in anterior teeth. In such cases, the use of indirect anchorage for retraction along with closing loops with torque or long-lever arms [20] is highly recommended.
In patients with class III malocclusion, usually class III elastics are used during orthodontic treatment. Spena et al. [21] have suggested that anterior brackets in anterior maxilla be placed in reverse so that maxillary incisors would have better inclination after treatment. By assuming a fixed position for the incisal edge, a decrease in torque in upper incisors results in a decrease in the space occupied by six anterior teeth, helping correct class III canine relationship.
In the lower jaw, due to the small number of changes in space, they do not have any clinical effects; however, they might be effective in the relapse of the results of treatment. Based on Schaeffer et al. [22] study on the growth, incisal movement patterns might be seen in three forms with aging and due to the residual growth including an increase in inclination, a decrease in inclination, and no change in inclination. In cases in which fixed and long-term retainers are not used for retention, these changes in inclination lead to isolated tooth rotati-on and finally to crowding.
Apart from esthetic considerations, based on the hypothesis of Reed and Holdaway [23], bodily retraction of upper incisors results in a greater decrease in SNA angle, which improves the outcomes from stability points of view. Therefore, stripping of lower teeth is not sufficient for only compensating extra space resulting from a decrease in torque.
On the other hand, a decrease in torque increases the patient's bite. If the contact of the incisal edge of anterior teeth is transferred from the lower part of cingulum to a point on the cingulum due to a decrease in torque, the amount of space occupied by six anterior teeth will suddenly decrease up to 6mm (Table 3), which cannot be compensated by stripping in the lower jaw. Therefore, striping is not advisable in extraction cases in the lower jaw except for cases such as the presence of anterior Bolton discrepancy. However, usually in cases in which no extraction is carried out in the lower jaw, stripping is more acceptable by the patients.

Conclusion
The results of the present study showed that changes in anterior torque affect changes in the space occupied by anterior teeth. The greatest changes were observed in the cingulum area of the anterior teeth. Changes were lower in teeth with triangular crowns. No significant differences were observed in changes, regarding tooth sizes.